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[h] Year 6 Maths Position and Direction Study Flashcards

[q] Plotting Points in the First Quadrant

Coordinates are the location of a point. They are written as (x, y ) where the x coordinate is the distance along the x axis and the y coordinate is the distance up the y axis.

[a] The point (0,0) is called the origin. Points are marked with a dot or small cross.

[q] Plotting Points in the Four Quadrants

The grid can be extended past the origin into four quadrants to give negative numbers on the axes.

[a] Points are plotted in the same way as for the first quadrant except that the x and y values may be negative. This is called plotting points in four quadrants.

[q] Coordinates on a Line

Knowing the coordinates of points on a line will help you find missing coordinates.

[a] Example

Look at grid A below. Look at the coordinates of the points already plotted: (1,3), (2,3), (3,3), (4,3). You will notice that the y coordinate is always 3. So, if you plot another point on this line, its y coordinate will be 3.

Look at grid B. Look at the coordinates of the points already plotted: (4,2), (4,3), (4,4), (4,5). You will notice that the x coordinate is always 4. So, if you plot another point on this line, its x coordinate will be 4.

[q] Translating Points

You can move points across and up or down a coordinate grid. This is called translation.

[a] When you mark the translated points, you add’ after the letter, for example A’, B’, C’.

If you move point A (–10,8) 20 units right and 7 units up, what will the coordinates of the new point A’ be?

[q] Translating Shapes

You can translate whole shapes by moving each point in turn.

[a] Example

Translate triangle A 2 squares right and 3 squares up.

By translating each point of the triangle in turn, you can plot the position of the new triangle A’.

[q] Reflecting Points and Shapes in the x Axis

You can use the axes of a coordinate grid as lines to reflect shapes. This is called reflection.

[a] A shape can be reflected in the x axis.

Reflect triangle A in the x axis to produce a new triangle A’.

[q] Reflecting Points and Shapes in the y Axis

A shape can be reflected in the y axis.

[a] The vertices of the reflected shape are the same distance from the y axis as the vertices of the original shape – again, they are just on the other side of the axis.

Reflect triangle A in the y axis to produce a new triangle A’’.

[q] Finding Missing Coordinates

You can find missing coordinates by using your knowledge of shapes.

[a] Example

Shape ABCD is a parallelogram. What are the coordinates of point D?

Plot point D at (–5,–10).

[q] Unlabelled Axes

Sometimes the axes are not labelled with numbers and there is no grid. However, it’s still possible to work out the missing coordinates.

[a] Example: ABCD is a square. What are the coordinates of point D?

From your knowledge of the properties of a square and what you know about coordinates in a line, you know that point D will have the same x coordinate as point A and the same y coordinate as point C. So the coordinates of point D are (3,1).

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